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President Obama, who insisted he would succeed where other presidents had failed to fix the nation’s health care system, now concedes that the effort might die in Congress.

The president’s newly conflicting signals could frustrate Democratic lawmakers who are hungry for guidance from the White House as they try to salvage the effort to extend coverage to millions of uninsured Americans and hold down spiraling medical costs.

Obama’s comments Thursday night came hours after Republican Scott Brown was sworn in to replace the late Edward M. Kennedy, leaving Democrats without their filibuster-proof majority in the Senate and Obama’s signature health legislation with no clear path forward.

“I think it’s very important for us to have a methodical, open process over the next several weeks, and then let’s go ahead and make a decision,’’ Obama said at a Democratic National Committee fundraiser.

“And it may be that . . . if Congress decides we’re not going to do it, even after all the facts are laid out, all the options are clear, then the American people can make a judgment as to whether this Congress has done the right thing for them or not,’’ the president said. “And that’s how democracy works. There will be elections coming up, and they’ll be able to make a determination and register their concerns.’’

It was a shift in tone for the issue the “Yes we can’’ candidate campaigned on and made the centerpiece of his domestic agenda last year.

In a speech to a joint session of Congress in September, Obama declared: “I am not the first president to take up this cause, but I am determined to be the last. . . . Here and now we will meet history’s test.’’

Sweeping health legislation to extend medical coverage to more than 30 million uninsured Americans passed the House and Senate last year and was on the verge of completion - though there were still disagreements between the two legislative bodies - before Brown’s upset victory last month in a special election in Massachusetts. Since then it has been in limbo, and Obama has not publicly offered specifics to help lawmakers move forward. Congressional aides felt his remarks Thursday did not clarify matters.

“The next step is what I announced at the State of the Union, which is to call on our Republican friends to present their ideas. What I’d like to do is have a meeting whereby I’m sitting with the Republicans, sitting with the Democrats, sitting with health care experts, and let’s just go through these bills. . . . And then I think that we’ve got to go ahead and move forward on a vote,’’ Obama said Thursday, shortly after a White House meeting with Democratic congressional leaders that produced no apparent progress on health care.

“I think we should be very deliberate, take our time. We’re going to be moving a jobs package forward over the next several weeks; that’s the thing that’s most urgent right now in the minds of Americans all across the country.’’

White House press secretary Robert Gibbs told reporters yesterday that there was no meeting set for the president to talk over health care strategy with Republican and Democratic lawmakers. The GOP has shown more interest in opposing Democrats on the issue than in working with them.